LMFDB - Embedded newform 728.2.i.a.701.16

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [728,2,Mod(701,728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(728, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("728.701"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.i (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			701.16
Character	$\chi$	$=$	728.701
Dual form			728.2.i.a.701.15

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.13101 + 0.849005i) q^{2} +0.208275i q^{3} +(0.558380 - 1.92047i) q^{4} +3.52272 q^{5} +(-0.176827 - 0.235562i) q^{6} +1.00000i q^{7} +(0.998957 + 2.64615i) q^{8} +2.95662 q^{9} +(-3.98424 + 2.99081i) q^{10} +1.92616 q^{11} +(0.399987 + 0.116297i) q^{12} +(3.39827 - 1.20488i) q^{13} +(-0.849005 - 1.13101i) q^{14} +0.733695i q^{15} +(-3.37642 - 2.14470i) q^{16} -3.54436 q^{17} +(-3.34398 + 2.51019i) q^{18} +0.129878 q^{19} +(1.96701 - 6.76528i) q^{20} -0.208275 q^{21} +(-2.17851 + 1.63532i) q^{22} -5.09962 q^{23} +(-0.551127 + 0.208058i) q^{24} +7.40954 q^{25} +(-2.82054 + 4.24789i) q^{26} +1.24062i q^{27} +(1.92047 + 0.558380i) q^{28} -6.31068i q^{29} +(-0.622911 - 0.829818i) q^{30} +1.15279i q^{31} +(5.63964 - 0.440915i) q^{32} +0.401171i q^{33} +(4.00871 - 3.00918i) q^{34} +3.52272i q^{35} +(1.65092 - 5.67811i) q^{36} -0.300461 q^{37} +(-0.146894 + 0.110267i) q^{38} +(0.250947 + 0.707776i) q^{39} +(3.51904 + 9.32162i) q^{40} -2.93462i q^{41} +(0.235562 - 0.176827i) q^{42} -5.57927i q^{43} +(1.07553 - 3.69913i) q^{44} +10.4153 q^{45} +(5.76773 - 4.32960i) q^{46} +2.30877i q^{47} +(0.446689 - 0.703226i) q^{48} -1.00000 q^{49} +(-8.38028 + 6.29074i) q^{50} -0.738202i q^{51} +(-0.416414 - 7.19907i) q^{52} +11.5827i q^{53} +(-1.05329 - 1.40315i) q^{54} +6.78531 q^{55} +(-2.64615 + 0.998957i) q^{56} +0.0270504i q^{57} +(5.35780 + 7.13746i) q^{58} -7.08922 q^{59} +(1.40904 + 0.409680i) q^{60} -6.22897i q^{61} +(-0.978728 - 1.30382i) q^{62} +2.95662i q^{63} +(-6.00417 + 5.28677i) q^{64} +(11.9712 - 4.24446i) q^{65} +(-0.340596 - 0.453729i) q^{66} -8.04110 q^{67} +(-1.97910 + 6.80684i) q^{68} -1.06212i q^{69} +(-2.99081 - 3.98424i) q^{70} +16.5533i q^{71} +(2.95354 + 7.82365i) q^{72} +11.4665i q^{73} +(0.339825 - 0.255093i) q^{74} +1.54322i q^{75} +(0.0725211 - 0.249427i) q^{76} +1.92616i q^{77} +(-0.884730 - 0.587449i) q^{78} +14.6896 q^{79} +(-11.8942 - 7.55519i) q^{80} +8.61147 q^{81} +(2.49151 + 3.31910i) q^{82} +3.76948 q^{83} +(-0.116297 + 0.399987i) q^{84} -12.4858 q^{85} +(4.73683 + 6.31022i) q^{86} +1.31436 q^{87} +(1.92415 + 5.09689i) q^{88} +0.982458i q^{89} +(-11.7799 + 8.84268i) q^{90} +(1.20488 + 3.39827i) q^{91} +(-2.84752 + 9.79368i) q^{92} -0.240098 q^{93} +(-1.96016 - 2.61125i) q^{94} +0.457523 q^{95} +(0.0918317 + 1.17460i) q^{96} -9.30657i q^{97} +(1.13101 - 0.849005i) q^{98} +5.69492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) $ 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$1$	$-1$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.13101	+	0.849005i	−0.799747	+	0.600337i
$2$	−1.13101	+	0.849005i	−0.799747	+	0.600337i
$3$			0.208275i			0.120248i	0.998191	+	0.0601239i	$0.0191496\pi$
$3$			0.208275i			0.120248i	−0.998191	+	0.0601239i	$0.980850\pi$
$4$	0.558380	−	1.92047i	0.279190	−	0.960236i
$5$	3.52272			1.57541			0.787704	−	0.616055i	$-0.211270\pi$
$5$	3.52272			1.57541			0.787704	+	0.616055i	$0.211270\pi$
$6$	−0.176827	−	0.235562i	−0.0721893	−	0.0961678i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	0.998957	+	2.64615i	0.353185	+	0.935554i
$9$	2.95662			0.985540
$10$	−3.98424	+	2.99081i	−1.25993	+	0.945776i
$11$	1.92616			0.580758			0.290379	−	0.956912i	$-0.406219\pi$
$11$	1.92616			0.580758			0.290379	+	0.956912i	$0.406219\pi$
$12$	0.399987	+	0.116297i	0.115466	+	0.0335720i
$13$	3.39827	−	1.20488i	0.942511	−	0.334174i
$13$	3.39827	−	1.20488i	0.942511	−	0.334174i
$14$	−0.849005	−	1.13101i	−0.226906	−	0.302276i
$15$			0.733695i			0.189439i
$16$	−3.37642	−	2.14470i	−0.844106	−	0.536176i
$17$	−3.54436			−0.859633			−0.429816	−	0.902916i	$-0.641422\pi$
$17$	−3.54436			−0.859633			−0.429816	+	0.902916i	$0.641422\pi$
$18$	−3.34398	+	2.51019i	−0.788183	+	0.591657i
$19$	0.129878			0.0297960			0.0148980	−	0.999889i	$-0.495258\pi$
$19$	0.129878			0.0297960			0.0148980	+	0.999889i	$0.495258\pi$
$20$	1.96701	−	6.76528i	0.439838	−	1.51276i
$21$	−0.208275			−0.0454494
$22$	−2.17851	+	1.63532i	−0.464459	+	0.348651i
$23$	−5.09962			−1.06334			−0.531672	−	0.846950i	$-0.678436\pi$
$23$	−5.09962			−1.06334			−0.531672	+	0.846950i	$0.678436\pi$
$24$	−0.551127	+	0.208058i	−0.112498	+	0.0424697i
$25$	7.40954			1.48191
$26$	−2.82054	+	4.24789i	−0.553153	+	0.833079i
$27$			1.24062i			0.238757i
$28$	1.92047	+	0.558380i	0.362935	+	0.105524i
$29$		−	6.31068i		−	1.17186i	−0.810360	−	0.585932i	$-0.800729\pi$
$29$		−	6.31068i		−	1.17186i	0.810360	−	0.585932i	$-0.199271\pi$
$30$	−0.622911	−	0.829818i	−0.113727	−	0.151503i
$31$			1.15279i			0.207048i	0.994627	+	0.103524i	$0.0330118\pi$
$31$			1.15279i			0.207048i	−0.994627	+	0.103524i	$0.966988\pi$
$32$	5.63964	−	0.440915i	0.996958	−	0.0779435i
$33$			0.401171i			0.0698349i
$34$	4.00871	−	3.00918i	0.687489	−	0.516070i
$35$			3.52272i			0.595448i
$36$	1.65092	−	5.67811i	0.275153	−	0.946351i
$37$	−0.300461			−0.0493954			−0.0246977	−	0.999695i	$-0.507862\pi$
$37$	−0.300461			−0.0493954			−0.0246977	+	0.999695i	$0.507862\pi$
$38$	−0.146894	+	0.110267i	−0.0238293	+	0.0178877i
$39$	0.250947	+	0.707776i	0.0401837	+	0.113335i
$40$	3.51904	+	9.32162i	0.556409	+	1.47388i
$41$		−	2.93462i		−	0.458311i	−0.973390	−	0.229156i	$-0.926404\pi$
$41$		−	2.93462i		−	0.458311i	0.973390	−	0.229156i	$-0.0735964\pi$
$42$	0.235562	−	0.176827i	0.0363480	−	0.0272850i
$43$		−	5.57927i		−	0.850830i	−0.904998	−	0.425415i	$-0.860128\pi$
$43$		−	5.57927i		−	0.850830i	0.904998	−	0.425415i	$-0.139872\pi$
$44$	1.07553	−	3.69913i	0.162142	−	0.557665i
$45$	10.4153			1.55263
$46$	5.76773	−	4.32960i	0.850406	−	0.638365i
$47$			2.30877i			0.336769i	0.985721	+	0.168384i	$0.0538549\pi$
$47$			2.30877i			0.336769i	−0.985721	+	0.168384i	$0.946145\pi$
$48$	0.446689	−	0.703226i	0.0644740	−	0.101502i
$49$	−1.00000			−0.142857
$50$	−8.38028	+	6.29074i	−1.18515	+	0.889645i
$51$		−	0.738202i		−	0.103369i
$52$	−0.416414	−	7.19907i	−0.0577462	−	0.998331i
$53$			11.5827i			1.59101i	0.605946	+	0.795506i	$0.292795\pi$
$53$			11.5827i			1.59101i	−0.605946	+	0.795506i	$0.707205\pi$
$54$	−1.05329	−	1.40315i	−0.143335	−	0.190945i
$55$	6.78531			0.914930
$56$	−2.64615	+	0.998957i	−0.353606	+	0.133491i
$57$			0.0270504i			0.00358291i
$58$	5.35780	+	7.13746i	0.703514	+	0.937195i
$59$	−7.08922			−0.922938			−0.461469	−	0.887156i	$-0.652677\pi$
$59$	−7.08922			−0.922938			−0.461469	+	0.887156i	$0.652677\pi$
$60$	1.40904	+	0.409680i	0.181906	+	0.0528895i
$61$		−	6.22897i		−	0.797538i	−0.917051	−	0.398769i	$-0.869438\pi$
$61$		−	6.22897i		−	0.797538i	0.917051	−	0.398769i	$-0.130562\pi$
$62$	−0.978728	−	1.30382i	−0.124299	−	0.165586i
$63$			2.95662i			0.372499i
$64$	−6.00417	+	5.28677i	−0.750521	+	0.660846i
$65$	11.9712	−	4.24446i	1.48484	−	0.526460i
$66$	−0.340596	−	0.453729i	−0.0419245	−	0.0558502i
$67$	−8.04110			−0.982376			−0.491188	−	0.871053i	$-0.663437\pi$
$67$	−8.04110			−0.982376			−0.491188	+	0.871053i	$0.663437\pi$
$68$	−1.97910	+	6.80684i	−0.240001	+	0.825450i
$69$		−	1.06212i		−	0.127865i
$70$	−2.99081	−	3.98424i	−0.357470	−	0.476208i
$71$			16.5533i			1.96452i	0.187535	+	0.982258i	$0.439950\pi$
$71$			16.5533i			1.96452i	−0.187535	+	0.982258i	$0.560050\pi$
$72$	2.95354	+	7.82365i	0.348078	+	0.922026i
$73$			11.4665i			1.34205i	0.741436	+	0.671024i	$0.234145\pi$
$73$			11.4665i			1.34205i	−0.741436	+	0.671024i	$0.765855\pi$
$74$	0.339825	−	0.255093i	0.0395038	−	0.0296539i
$75$			1.54322i			0.178196i
$76$	0.0725211	−	0.249427i	0.00831875	−	0.0286112i
$77$			1.92616i			0.219506i
$78$	−0.884730	−	0.587449i	−0.100176	−	0.0665155i
$79$	14.6896			1.65271			0.826357	−	0.563147i	$-0.190409\pi$
$79$	14.6896			1.65271			0.826357	+	0.563147i	$0.190409\pi$
$80$	−11.8942	−	7.55519i	−1.32981	−	0.844696i
$81$	8.61147			0.956830
$82$	2.49151	+	3.31910i	0.275141	+	0.366533i
$83$	3.76948			0.413754			0.206877	−	0.978367i	$-0.433670\pi$
$83$	3.76948			0.413754			0.206877	+	0.978367i	$0.433670\pi$
$84$	−0.116297	+	0.399987i	−0.0126890	+	0.0436421i
$85$	−12.4858			−1.35427
$86$	4.73683	+	6.31022i	0.510785	+	0.680449i
$87$	1.31436			0.140914
$88$	1.92415	+	5.09689i	0.205115	+	0.543330i
$89$			0.982458i			0.104140i	0.998643	+	0.0520702i	$0.0165820\pi$
$89$			0.982458i			0.104140i	−0.998643	+	0.0520702i	$0.983418\pi$
$90$	−11.7799	+	8.84268i	−1.24171	+	0.932100i
$91$	1.20488	+	3.39827i	0.126306	+	0.356236i
$92$	−2.84752	+	9.79368i	−0.296875	+	1.02106i
$93$	−0.240098			−0.0248970
$94$	−1.96016	−	2.61125i	−0.202175	−	0.269330i
$95$	0.457523			0.0469409
$96$	0.0918317	+	1.17460i	0.00937253	+	0.119882i
$97$		−	9.30657i		−	0.944939i	−0.881347	−	0.472469i	$-0.843363\pi$
$97$		−	9.30657i		−	0.944939i	0.881347	−	0.472469i	$-0.156637\pi$
$98$	1.13101	−	0.849005i	0.114250	−	0.0857625i
$99$	5.69492			0.572361
$100$	4.13733	−	14.2298i	0.413733	−	1.42298i
$101$			9.15160i			0.910618i	0.890333	+	0.455309i	$0.150471\pi$
$101$			9.15160i			0.910618i	−0.890333	+	0.455309i	$0.849529\pi$
$102$	0.626738	+	0.834916i	0.0620563	+	0.0826690i
$103$	5.49996			0.541927			0.270964	−	0.962590i	$-0.412658\pi$
$103$	5.49996			0.541927			0.270964	+	0.962590i	$0.412658\pi$
$104$	6.58302	+	7.78870i	0.645518	+	0.763745i
$105$	−0.733695			−0.0716013
$106$	−9.83381	−	13.1002i	−0.955144	−	1.27241i
$107$		−	6.53885i		−	0.632134i	−0.948737	−	0.316067i	$-0.897637\pi$
$107$		−	6.53885i		−	0.632134i	0.948737	−	0.316067i	$-0.102363\pi$
$108$	2.38257	+	0.692735i	0.229263	+	0.0666585i
$109$	−12.0875			−1.15778			−0.578888	−	0.815407i	$-0.696513\pi$
$109$	−12.0875			−1.15778			−0.578888	+	0.815407i	$0.696513\pi$
$110$	−7.67427	+	5.76076i	−0.731713	+	0.549267i
$111$		−	0.0625785i		−	0.00593969i
$112$	2.14470	−	3.37642i	0.202656	−	0.319042i
$113$	−4.68304			−0.440543			−0.220272	−	0.975439i	$-0.570694\pi$
$113$	−4.68304			−0.440543			−0.220272	+	0.975439i	$0.570694\pi$
$114$	−0.0229659	−	0.0305943i	−0.00215095	−	0.00286542i
$115$	−17.9645			−1.67520
$116$	−12.1195	−	3.52376i	−1.12527	−	0.327172i
$117$	10.0474	−	3.56238i	0.928883	−	0.329342i
$118$	8.01800	−	6.01879i	0.738117	−	0.554074i
$119$		−	3.54436i		−	0.324911i
$120$	−1.94146	+	0.732929i	−0.177231	+	0.0669070i
$121$	−7.28992			−0.662720
$122$	5.28843	+	7.04504i	0.478792	+	0.637828i
$123$	0.611209			0.0551109
$124$	2.21391	+	0.643696i	0.198815	+	0.0578056i
$125$	8.48812			0.759200
$126$	−2.51019	−	3.34398i	−0.223625	−	0.297905i
$127$	−14.7640			−1.31009			−0.655045	−	0.755590i	$-0.727350\pi$
$127$	−14.7640			−1.31009			−0.655045	+	0.755590i	$0.727350\pi$
$128$	2.30230	−	11.0770i	0.203496	−	0.979076i
$129$	1.16202			0.102310
$130$	−9.93596	+	14.9641i	−0.871442	+	1.31244i
$131$		−	15.8504i		−	1.38486i	−0.721487	−	0.692428i	$-0.756541\pi$
$131$		−	15.8504i		−	1.38486i	0.721487	−	0.692428i	$-0.243459\pi$
$132$	0.770437	+	0.224006i	0.0670580	+	0.0194972i
$133$			0.129878i			0.0112618i
$134$	9.09458	−	6.82694i	0.785652	−	0.589757i
$135$			4.37034i			0.376139i
$136$	−3.54066	−	9.37888i	−0.303609	−	0.804233i
$137$		−	8.39453i		−	0.717193i	−0.933493	−	0.358596i	$-0.883255\pi$
$137$		−	8.39453i		−	0.717193i	0.933493	−	0.358596i	$-0.116745\pi$
$138$	0.901750	+	1.20128i	0.0767620	+	0.102259i
$139$		−	13.5249i		−	1.14716i	−0.819149	−	0.573581i	$-0.805554\pi$
$139$		−	13.5249i		−	1.14716i	0.819149	−	0.573581i	$-0.194446\pi$
$140$	6.76528	+	1.96701i	0.571770	+	0.166243i
$141$	−0.480859			−0.0404957
$142$	−14.0538	−	18.7220i	−1.17937	−	1.57112i
$143$	6.54561	−	2.32079i	0.547371	−	0.194074i
$144$	−9.98281	−	6.34108i	−0.831901	−	0.528423i
$145$		−	22.2307i		−	1.84616i
$146$	−9.73509	−	12.9687i	−0.805681	−	1.07330i
$147$		−	0.208275i		−	0.0171783i
$148$	−0.167771	+	0.577026i	−0.0137907	+	0.0474312i
$149$	19.3528			1.58545			0.792723	−	0.609582i	$-0.208663\pi$
$149$	19.3528			1.58545			0.792723	+	0.609582i	$0.208663\pi$
$150$	−1.31021	−	1.74541i	−0.106978	−	0.142512i
$151$		−	5.55900i		−	0.452385i	−0.974083	−	0.226193i	$-0.927372\pi$
$151$		−	5.55900i		−	0.452385i	0.974083	−	0.226193i	$-0.0726279\pi$
$152$	0.129742	+	0.343676i	0.0105235	+	0.0278758i
$153$	−10.4793			−0.847203
$154$	−1.63532	−	2.17851i	−0.131778	−	0.175549i
$155$			4.06096i			0.326184i
$156$	1.49939	−	0.0867287i	0.120047	−	0.00694385i
$157$			16.1401i			1.28812i	0.764974	+	0.644061i	$0.222752\pi$
$157$			16.1401i			1.28812i	−0.764974	+	0.644061i	$0.777248\pi$
$158$	−16.6142	+	12.4716i	−1.32175	+	0.992186i
$159$	−2.41240			−0.191316
$160$	19.8669	−	1.55322i	1.57061	−	0.122793i
$161$		−	5.09962i		−	0.401906i
$162$	−9.73969	+	7.31119i	−0.765222	+	0.574421i
$163$	−3.76604			−0.294979			−0.147490	−	0.989064i	$-0.547119\pi$
$163$	−3.76604			−0.294979			−0.147490	+	0.989064i	$0.547119\pi$
$164$	−5.63586	−	1.63863i	−0.440087	−	0.127956i
$165$			1.41321i			0.110018i
$166$	−4.26333	+	3.20031i	−0.330899	+	0.248392i
$167$			23.2916i			1.80236i	0.433449	+	0.901178i	$0.357296\pi$
$167$			23.2916i			1.80236i	−0.433449	+	0.901178i	$0.642704\pi$
$168$	−0.208058	−	0.551127i	−0.0160520	−	0.0425203i
$169$	10.0965	−	8.18903i	0.776656	−	0.629925i
$170$	14.1216	−	10.6005i	1.08307	−	0.813020i
$171$	0.384000			0.0293652
$172$	−10.7148	−	3.11535i	−0.816998	−	0.237543i
$173$			19.8402i			1.50842i	0.656633	+	0.754210i	$0.271980\pi$
$173$			19.8402i			1.50842i	−0.656633	+	0.754210i	$0.728020\pi$
$174$	−1.48656	+	1.11590i	−0.112696	+	0.0845960i
$175$			7.40954i			0.560108i
$176$	−6.50352	−	4.13104i	−0.490222	−	0.311389i
$177$		−	1.47651i		−	0.110981i
$178$	−0.834112	−	1.11117i	−0.0625194	−	0.0832859i
$179$		−	0.396420i		−	0.0296298i	−0.999890	−	0.0148149i	$-0.995284\pi$
$179$		−	0.396420i		−	0.0296298i	0.999890	−	0.0148149i	$-0.00471591\pi$
$180$	5.81571	−	20.0024i	0.433478	−	1.49089i
$181$		−	21.0449i		−	1.56425i	−0.623121	−	0.782126i	$-0.714135\pi$
$181$		−	21.0449i		−	1.56425i	0.623121	−	0.782126i	$-0.285865\pi$
$182$	−4.24789	−	2.82054i	−0.314874	−	0.209072i
$183$	1.29734			0.0959022
$184$	−5.09430	−	13.4943i	−0.375557	−	0.994816i
$185$	−1.05844			−0.0778179
$186$	0.271554	−	0.203845i	0.0199113	−	0.0149466i
$187$	−6.82699			−0.499239
$188$	4.43393	+	1.28917i	0.323377	+	0.0940223i
$189$	−1.24062			−0.0902416
$190$	−0.517464	+	0.388440i	−0.0375408	+	0.0281804i
$191$	5.37919			0.389225			0.194612	−	0.980880i	$-0.437655\pi$
$191$	5.37919			0.389225			0.194612	+	0.980880i	$0.437655\pi$
$192$	−1.10110	−	1.25052i	−0.0794653	−	0.0902485i
$193$		−	23.0841i		−	1.66163i	−0.556548	−	0.830816i	$-0.687874\pi$
$193$		−	23.0841i		−	1.66163i	0.556548	−	0.830816i	$-0.312126\pi$
$194$	7.90133	+	10.5258i	0.567282	+	0.755712i
$195$	0.884015	+	2.49330i	0.0633056	+	0.178549i
$196$	−0.558380	+	1.92047i	−0.0398843	+	0.137177i
$197$	8.31831			0.592655			0.296328	−	0.955086i	$-0.404238\pi$
$197$	8.31831			0.592655			0.296328	+	0.955086i	$0.404238\pi$
$198$	−6.44102	+	4.83502i	−0.457744	+	0.343610i
$199$	−18.8463			−1.33598			−0.667989	−	0.744171i	$-0.732845\pi$
$199$	−18.8463			−1.33598			−0.667989	+	0.744171i	$0.732845\pi$
$200$	7.40181	+	19.6067i	0.523387	+	1.38640i
$201$		−	1.67476i		−	0.118129i
$202$	−7.76976	−	10.3506i	−0.546678	−	0.728264i
$203$	6.31068			0.442923
$204$	−1.41770	−	0.412197i	−0.0992586	−	0.0288596i
$205$		−	10.3378i		−	0.722026i
$206$	−6.22053	+	4.66950i	−0.433405	+	0.325339i
$207$	−15.0776			−1.04797
$208$	−14.0581	−	3.22010i	−0.974756	−	0.223274i
$209$	0.250165			0.0173043
$210$	0.829818	−	0.622911i	0.0572629	−	0.0429849i
$211$		−	19.4654i		−	1.34005i	−0.742337	−	0.670027i	$-0.766283\pi$
$211$		−	19.4654i		−	1.34005i	0.742337	−	0.670027i	$-0.233717\pi$
$212$	22.2443	+	6.46757i	1.52775	+	0.444194i
$213$	−3.44764			−0.236229
$214$	5.55152	+	7.39552i	0.379494	+	0.505548i
$215$		−	19.6542i		−	1.34040i
$216$	−3.28285	+	1.23932i	−0.223370	+	0.0843252i
$217$	−1.15279			−0.0782567
$218$	13.6712	−	10.2624i	0.925928	−	0.695057i
$219$	−2.38818			−0.161378
$220$	3.78878	−	13.0310i	0.255439	−	0.878549i
$221$	−12.0447	+	4.27053i	−0.810214	+	0.287267i
$222$	0.0531295	+	0.0707771i	0.00356582	+	0.00475025i
$223$			17.6477i			1.18178i	0.806753	+	0.590889i	$0.201223\pi$
$223$			17.6477i			1.18178i	−0.806753	+	0.590889i	$0.798777\pi$
$224$	0.440915	+	5.63964i	0.0294599	+	0.376815i
$225$	21.9072			1.46048
$226$	5.29658	−	3.97593i	0.352323	−	0.264475i
$227$	−18.0842			−1.20029			−0.600144	−	0.799892i	$-0.704890\pi$
$227$	−18.0842			−1.20029			−0.600144	+	0.799892i	$0.704890\pi$
$228$	0.0519494	+	0.0151044i	0.00344044	+	0.00100031i
$229$	−4.25750			−0.281343			−0.140672	−	0.990056i	$-0.544926\pi$
$229$	−4.25750			−0.281343			−0.140672	+	0.990056i	$0.544926\pi$
$230$	20.3181	−	15.2520i	1.33974	−	1.00569i
$231$	−0.401171			−0.0263951
$232$	16.6990	−	6.30410i	1.09634	−	0.413884i
$233$	−12.0468			−0.789210			−0.394605	−	0.918851i	$-0.629119\pi$
$233$	−12.0468			−0.789210			−0.394605	+	0.918851i	$0.629119\pi$
$234$	−8.33927	+	12.5594i	−0.545155	+	0.821033i
$235$			8.13314i			0.530547i
$236$	−3.95848	+	13.6147i	−0.257675	+	0.886238i
$237$			3.05949i			0.198735i
$238$	3.00918	+	4.00871i	0.195056	+	0.259846i
$239$			1.26186i			0.0816230i	0.999167	+	0.0408115i	$0.0129943\pi$
$239$			1.26186i			0.0816230i	−0.999167	+	0.0408115i	$0.987006\pi$
$240$	1.57356	−	2.47727i	0.101573	−	0.159907i
$241$			16.9944i			1.09471i	0.836902	+	0.547353i	$0.184364\pi$
$241$			16.9944i			1.09471i	−0.836902	+	0.547353i	$0.815636\pi$
$242$	8.24499	−	6.18918i	0.530008	−	0.397856i
$243$			5.51541i			0.353814i
$244$	−11.9626	−	3.47813i	−0.765825	−	0.222664i
$245$	−3.52272			−0.225058
$246$	−0.691286	+	0.518920i	−0.0440748	+	0.0330851i
$247$	0.441360	−	0.156487i	0.0280831	−	0.00995705i
$248$	−3.05046	+	1.15159i	−0.193704	+	0.0731261i
$249$			0.785089i			0.0497530i
$250$	−9.60017	+	7.20646i	−0.607168	+	0.455776i
$251$			16.4332i			1.03725i	0.855001	+	0.518626i	$0.173556\pi$
$251$			16.4332i			1.03725i	−0.855001	+	0.518626i	$0.826444\pi$
$252$	5.67811	+	1.65092i	0.357687	+	0.103998i
$253$	−9.82267			−0.617546
$254$	16.6982	−	12.5347i	1.04774	−	0.786496i
$255$		−	2.60048i		−	0.162848i
$256$	6.80049	+	14.4829i	0.425030	+	0.905179i
$257$	−18.6782			−1.16511			−0.582557	−	0.812790i	$-0.697948\pi$
$257$	−18.6782			−1.16511			−0.582557	+	0.812790i	$0.697948\pi$
$258$	−1.31426	+	0.986564i	−0.0818225	+	0.0614208i
$259$		−	0.300461i		−	0.0186697i
$260$	−1.46691	−	25.3603i	−0.0909738	−	1.57278i
$261$		−	18.6583i		−	1.15492i
$262$	13.4571	+	17.9270i	0.831380	+	1.10753i
$263$	−0.495204			−0.0305356			−0.0152678	−	0.999883i	$-0.504860\pi$
$263$	−0.495204			−0.0305356			−0.0152678	+	0.999883i	$0.504860\pi$
$264$	−1.06156	+	0.400752i	−0.0653343	+	0.0246646i
$265$			40.8027i			2.50649i
$266$	−0.110267	−	0.146894i	−0.00676090	−	0.00900662i
$267$	−0.204622			−0.0125226
$268$	−4.48998	+	15.4427i	−0.274269	+	0.943313i
$269$			10.0263i			0.611314i	0.952142	+	0.305657i	$0.0988760\pi$
$269$			10.0263i			0.611314i	−0.952142	+	0.305657i	$0.901124\pi$
$270$	−3.71045	−	4.94291i	−0.225810	−	0.300816i
$271$		−	19.8983i		−	1.20874i	−0.796705	−	0.604369i	$-0.793425\pi$
$271$		−	19.8983i		−	1.20874i	0.796705	−	0.604369i	$-0.206575\pi$
$272$	11.9673	+	7.60160i	0.725621	+	0.460915i
$273$	−0.707776	+	0.250947i	−0.0428366	+	0.0151880i
$274$	7.12700	+	9.49432i	0.430558	+	0.573573i
$275$	14.2719			0.860630
$276$	−2.03978	−	0.593069i	−0.122780	−	0.0356985i
$277$		−	29.0585i		−	1.74596i	−0.487759	−	0.872978i	$-0.662186\pi$
$277$		−	29.0585i		−	1.74596i	0.487759	−	0.872978i	$-0.337814\pi$
$278$	11.4827	+	15.2968i	0.688685	+	0.917440i
$279$			3.40837i			0.204054i
$280$	−9.32162	+	3.51904i	−0.557073	+	0.210303i
$281$			14.5021i			0.865120i	0.901605	+	0.432560i	$0.142390\pi$
$281$			14.5021i			0.865120i	−0.901605	+	0.432560i	$0.857610\pi$
$282$	0.543858	−	0.408252i	0.0323863	−	0.0243111i
$283$			5.54760i			0.329771i	0.986313	+	0.164885i	$0.0527254\pi$
$283$			5.54760i			0.329771i	−0.986313	+	0.164885i	$0.947275\pi$
$284$	31.7902	+	9.24303i	1.88640	+	0.548473i
$285$			0.0952907i			0.00564454i
$286$	−5.43280	+	8.18210i	−0.321248	+	0.483818i
$287$	2.93462			0.173225
$288$	16.6743	−	1.30362i	0.982542	−	0.0768164i
$289$	−4.43753			−0.261031
$290$	18.8740	+	25.1433i	1.10832	+	1.47646i
$291$	1.93833			0.113627
$292$	22.0210	+	6.40264i	1.28868	+	0.374686i
$293$	−24.7162			−1.44393			−0.721967	−	0.691928i	$-0.756762\pi$
$293$	−24.7162			−1.44393			−0.721967	+	0.691928i	$0.756762\pi$
$294$	0.176827	+	0.235562i	0.0103128	+	0.0137383i
$295$	−24.9733			−1.45400
$296$	−0.300147	−	0.795062i	−0.0174457	−	0.0462121i
$297$			2.38962i			0.138660i
$298$	−21.8883	+	16.4307i	−1.26796	+	0.951803i
$299$	−17.3299	+	6.14444i	−1.00221	+	0.355342i
$300$	2.96372	+	0.861704i	0.171110	+	0.0497505i
$301$	5.57927			0.321584
$302$	4.71963	+	6.28731i	0.271584	+	0.361794i
$303$	−1.90605			−0.109500
$304$	−0.438523	−	0.278550i	−0.0251510	−	0.0159759i
$305$		−	21.9429i		−	1.25645i
$306$	11.8522	−	8.89700i	0.677548	−	0.508608i
$307$	14.9768			0.854770			0.427385	−	0.904070i	$-0.359435\pi$
$307$	14.9768			0.854770			0.427385	+	0.904070i	$0.359435\pi$
$308$	3.69913	+	1.07553i	0.210777	+	0.0612838i
$309$			1.14551i			0.0651656i
$310$	−3.44778	−	4.59300i	−0.195821	−	0.260865i
$311$	−22.2304			−1.26057			−0.630284	−	0.776365i	$-0.717061\pi$
$311$	−22.2304			−1.26057			−0.630284	+	0.776365i	$0.717061\pi$
$312$	−1.62219	+	1.37108i	−0.0918387	+	0.0776221i
$313$	8.34646			0.471770			0.235885	−	0.971781i	$-0.424201\pi$
$313$	8.34646			0.471770			0.235885	+	0.971781i	$0.424201\pi$
$314$	−13.7030	−	18.2547i	−0.773308	−	1.03017i
$315$			10.4153i			0.586838i
$316$	8.20239	−	28.2110i	0.461421	−	1.58700i
$317$	19.6311			1.10260			0.551298	−	0.834309i	$-0.314133\pi$
$317$	19.6311			1.10260			0.551298	+	0.834309i	$0.314133\pi$
$318$	2.72845	−	2.04814i	0.153004	−	0.114854i
$319$		−	12.1554i		−	0.680570i
$320$	−21.1510	+	18.6238i	−1.18238	+	1.04110i
$321$	1.36188			0.0760128
$322$	4.32960	+	5.76773i	0.241279	+	0.321423i
$323$	−0.460334			−0.0256136
$324$	4.80847	−	16.5381i	0.267137	−	0.918783i
$325$	25.1796	−	8.92761i	1.39671	−	0.495215i
$326$	4.25944	−	3.19739i	0.235909	−	0.177087i
$327$		−	2.51754i		−	0.139220i
$328$	7.76544	−	2.93156i	0.428775	−	0.161868i
$329$	−2.30877			−0.127287
$330$	−1.19982	−	1.59836i	−0.0660482	−	0.0879868i
$331$	−33.6438			−1.84923			−0.924616	−	0.380900i	$-0.875614\pi$
$331$	−33.6438			−1.84923			−0.924616	+	0.380900i	$0.875614\pi$
$332$	2.10480	−	7.23918i	0.115516	−	0.397302i
$333$	−0.888348			−0.0486812
$334$	−19.7747	−	26.3431i	−1.08202	−	1.44143i
$335$	−28.3265			−1.54764
$336$	0.703226	+	0.446689i	0.0383641	+	0.0243689i
$337$	0.0143341			0.000780827			0.000390413	−	1.00000i	$-0.499876\pi$
$337$	0.0143341			0.000780827			0.000390413		1.00000i	$0.499876\pi$
$338$	−4.46677	+	17.8339i	−0.242960	+	0.970036i
$339$		−	0.975362i		−	0.0529744i
$340$	−6.97180	+	23.9786i	−0.378099	+	1.30042i
$341$			2.22046i			0.120245i
$342$	−0.434309	+	0.326018i	−0.0234847	+	0.0176290i
$343$		−	1.00000i		−	0.0539949i
$344$	14.7636	−	5.57345i	0.795998	−	0.300500i
$345$		−	3.74157i		−	0.201439i
$346$	−16.8444	−	22.4395i	−0.905561	−	1.20635i
$347$			3.13277i			0.168176i	0.996458	+	0.0840880i	$0.0267977\pi$
$347$			3.13277i			0.168176i	−0.996458	+	0.0840880i	$0.973202\pi$
$348$	0.733911	−	2.52419i	0.0393418	−	0.135311i
$349$	1.24421			0.0666011			0.0333006	−	0.999445i	$-0.489398\pi$
$349$	1.24421			0.0666011			0.0333006	+	0.999445i	$0.489398\pi$
$350$	−6.29074	−	8.38028i	−0.336254	−	0.447945i
$351$	1.49480	+	4.21596i	0.0797863	+	0.225031i
$352$	10.8628	−	0.849271i	0.578991	−	0.0452663i
$353$		−	7.40604i		−	0.394184i	−0.980385	−	0.197092i	$-0.936850\pi$
$353$		−	7.40604i		−	0.394184i	0.980385	−	0.197092i	$-0.0631497\pi$
$354$	1.25356	+	1.66995i	0.0666262	+	0.0887569i
$355$			58.3126i			3.09491i
$356$	1.88678	+	0.548585i	0.0999993	+	0.0290749i
$357$	0.738202			0.0390698
$358$	0.336563	+	0.448356i	0.0177879	+	0.0236964i
$359$		−	36.1561i		−	1.90824i	−0.299418	−	0.954122i	$-0.596792\pi$
$359$		−	36.1561i		−	1.90824i	0.299418	−	0.954122i	$-0.403208\pi$
$360$	10.4045	+	27.5605i	0.548364	+	1.45257i
$361$	−18.9831			−0.999112
$362$	17.8672	+	23.8020i	0.939079	+	1.25101i
$363$		−	1.51831i		−	0.0796906i
$364$	7.19907	−	0.416414i	0.377334	−	0.0218260i
$365$			40.3931i			2.11427i
$366$	−1.46731	+	1.10145i	−0.0766974	+	0.0575737i
$367$	8.10201			0.422922			0.211461	−	0.977386i	$-0.432178\pi$
$367$	8.10201			0.422922			0.211461	+	0.977386i	$0.432178\pi$
$368$	17.2185	+	10.9372i	0.897575	+	0.570140i
$369$		−	8.67657i		−	0.451684i
$370$	1.19711	−	0.898619i	0.0622346	−	0.0467170i
$371$	−11.5827			−0.601346
$372$	−0.134066	+	0.461102i	−0.00695100	+	0.0239070i
$373$			7.73552i			0.400530i	0.979742	+	0.200265i	$0.0641803\pi$
$373$			7.73552i			0.400530i	−0.979742	+	0.200265i	$0.935820\pi$
$374$	7.72141	−	5.79615i	0.399265	−	0.299712i
$375$			1.76787i			0.0912922i
$376$	−6.10934	+	2.30636i	−0.315065	+	0.118941i
$377$	−7.60362	−	21.4454i	−0.391606	−	1.10450i
$378$	1.40315	−	1.05329i	0.0721704	−	0.0541754i
$379$	32.4599			1.66735			0.833675	−	0.552255i	$-0.186232\pi$
$379$	32.4599			1.66735			0.833675	+	0.552255i	$0.186232\pi$
$380$	0.255471	−	0.878660i	0.0131054	−	0.0450743i
$381$		−	3.07497i		−	0.157535i
$382$	−6.08394	+	4.56696i	−0.311281	+	0.233666i
$383$			35.7865i			1.82860i	0.405032	+	0.914302i	$0.367260\pi$
$383$			35.7865i			1.82860i	−0.405032	+	0.914302i	$0.632740\pi$
$384$	2.30706	+	0.479512i	0.117732	+	0.0244700i
$385$			6.78531i			0.345811i
$386$	19.5985	+	26.1084i	0.997540	+	1.32888i
$387$		−	16.4958i		−	0.838528i
$388$	−17.8730	−	5.19660i	−0.907364	−	0.263817i
$389$			6.32180i			0.320528i	0.987074	+	0.160264i	$0.0512345\pi$
$389$			6.32180i			0.320528i	−0.987074	+	0.160264i	$0.948765\pi$
$390$	−3.11665	−	2.06942i	−0.157818	−	0.104789i
$391$	18.0749			0.914086
$392$	−0.998957	−	2.64615i	−0.0504549	−	0.133651i
$393$	3.30124			0.166526
$394$	−9.40812	+	7.06229i	−0.473974	+	0.355793i
$395$	51.7474			2.60370
$396$	3.17992	−	10.9369i	0.159797	−	0.549601i
$397$	−10.2742			−0.515649			−0.257824	−	0.966192i	$-0.583006\pi$
$397$	−10.2742			−0.515649			−0.257824	+	0.966192i	$0.583006\pi$
$398$	21.3154	−	16.0006i	1.06844	−	0.802038i
$399$	−0.0270504			−0.00135421
$400$	−25.0177	−	15.8913i	−1.25089	−	0.794563i
$401$		−	1.79881i		−	0.0898285i	−0.998991	−	0.0449142i	$-0.985699\pi$
$401$		−	1.79881i		−	0.0898285i	0.998991	−	0.0449142i	$-0.0143015\pi$
$402$	1.42188	+	1.89418i	0.0709170	+	0.0944730i
$403$	1.38898	+	3.91751i	0.0691899	+	0.195145i
$404$	17.5754	+	5.11007i	0.874408	+	0.254235i
$405$	30.3358			1.50740
$406$	−7.13746	+	5.35780i	−0.354226	+	0.265903i
$407$	−0.578734			−0.0286868
$408$	1.95339	−	0.737432i	0.0967072	−	0.0365083i
$409$			21.9102i			1.08339i	0.840575	+	0.541696i	$0.182217\pi$
$409$			21.9102i			1.08339i	−0.840575	+	0.541696i	$0.817783\pi$
$410$	8.77689	+	11.6922i	0.433460	+	0.577438i
$411$	1.74837			0.0862409
$412$	3.07107	−	10.5625i	0.151301	−	0.520378i
$413$		−	7.08922i		−	0.348838i
$414$	17.0530	−	12.8010i	0.838110	−	0.629135i
$415$	13.2788			0.651831
$416$	18.6338	−	8.29345i	0.913597	−	0.406620i
$417$	2.81689			0.137944
$418$	−0.282940	+	0.212392i	−0.0138390	+	0.0103884i
$419$			18.8887i			0.922773i	0.887199	+	0.461386i	$0.152648\pi$
$419$			18.8887i			0.922773i	−0.887199	+	0.461386i	$0.847352\pi$
$420$	−0.409680	+	1.40904i	−0.0199903	+	0.0687541i
$421$	6.34070			0.309027			0.154513	−	0.987991i	$-0.450619\pi$
$421$	6.34070			0.309027			0.154513	+	0.987991i	$0.450619\pi$
$422$	16.5262	+	22.0156i	0.804484	+	1.07170i
$423$			6.82615i			0.331899i
$424$	−30.6496	+	11.5707i	−1.48848	+	0.561921i
$425$	−26.2620			−1.27390
$426$	3.89933	−	2.92707i	0.188923	−	0.141817i
$427$	6.22897			0.301441
$428$	−12.5577	−	3.65116i	−0.606998	−	0.176485i
$429$	0.483363	+	1.36329i	0.0233370	+	0.0658202i
$430$	16.6865	+	22.2291i	0.804695	+	1.07198i
$431$		−	27.2674i		−	1.31342i	−0.754141	−	0.656712i	$-0.771947\pi$
$431$		−	27.2674i		−	1.31342i	0.754141	−	0.656712i	$-0.228053\pi$
$432$	2.66076	−	4.18885i	0.128016	−	0.201536i
$433$	17.8959			0.860023			0.430012	−	0.902823i	$-0.358509\pi$
$433$	17.8959			0.860023			0.430012	+	0.902823i	$0.358509\pi$
$434$	1.30382	−	0.978728i	0.0625855	−	0.0469804i
$435$	4.63012			0.221997
$436$	−6.74944	+	23.2138i	−0.323239	+	1.11174i
$437$	−0.662328			−0.0316834
$438$	2.70106	−	2.02758i	0.129062	−	0.0968814i
$439$	16.4464			0.784944			0.392472	−	0.919764i	$-0.371620\pi$
$439$	16.4464			0.784944			0.392472	+	0.919764i	$0.371620\pi$
$440$	6.77823	+	17.9549i	0.323139	+	0.855967i
$441$	−2.95662			−0.140791
$442$	9.99700	−	15.0560i	0.475509	−	0.716142i
$443$		−	21.4873i		−	1.02089i	−0.859910	−	0.510446i	$-0.829480\pi$
$443$		−	21.4873i		−	1.02089i	0.859910	−	0.510446i	$-0.170520\pi$
$444$	−0.120180	−	0.0349426i	−0.00570350	−	0.00165830i
$445$			3.46092i			0.164063i
$446$	−14.9830	−	19.9598i	−0.709466	−	0.945123i
$447$			4.03072i			0.190646i
$448$	−5.28677	−	6.00417i	−0.249776	−	0.283670i
$449$			11.6297i			0.548840i	0.961610	+	0.274420i	$0.0884858\pi$
$449$			11.6297i			0.548840i	−0.961610	+	0.274420i	$0.911514\pi$
$450$	−24.7773	+	18.5993i	−1.16801	+	0.876781i
$451$		−	5.65254i		−	0.266168i
$452$	−2.61491	+	8.99365i	−0.122995	+	0.423026i
$453$	1.15780			0.0543983
$454$	20.4534	−	15.3536i	0.959926	−	0.720578i
$455$	4.24446	+	11.9712i	0.198983	+	0.561216i
$456$	−0.0715792	+	0.0270221i	−0.00335200	+	0.00126543i
$457$			20.1702i			0.943524i	0.881726	+	0.471762i	$0.156382\pi$
$457$			20.1702i			0.943524i	−0.881726	+	0.471762i	$0.843618\pi$
$458$	4.81529	−	3.61464i	0.225004	−	0.168901i
$459$		−	4.39719i		−	0.205243i
$460$	−10.0310	+	34.5004i	−0.467699	+	1.60859i
$461$	−15.3054			−0.712845			−0.356423	−	0.934325i	$-0.616004\pi$
$461$	−15.3054			−0.712845			−0.356423	+	0.934325i	$0.616004\pi$
$462$	0.453729	−	0.340596i	0.0211094	−	0.0158460i
$463$		−	22.3957i		−	1.04082i	−0.853917	−	0.520409i	$-0.825780\pi$
$463$		−	22.3957i		−	1.04082i	0.853917	−	0.520409i	$-0.174220\pi$
$464$	−13.5345	+	21.3075i	−0.628326	+	0.989178i
$465$	−0.845798			−0.0392230
$466$	13.6250	−	10.2278i	0.631168	−	0.473792i
$467$		−	10.1198i		−	0.468287i	−0.972202	−	0.234143i	$-0.924771\pi$
$467$		−	10.1198i		−	0.468287i	0.972202	−	0.234143i	$-0.0752285\pi$
$468$	−1.23118	−	21.2849i	−0.0569112	−	0.983896i
$469$		−	8.04110i		−	0.371303i
$470$	−6.90508	−	9.19868i	−0.318508	−	0.424304i
$471$	−3.36159			−0.154894
$472$	−7.08183	−	18.7591i	−0.325967	−	0.863458i
$473$		−	10.7465i		−	0.494127i
$474$	−2.59752	−	3.46032i	−0.119308	−	0.158938i
$475$	0.962335			0.0441550
$476$	−6.80684	−	1.97910i	−0.311991	−	0.0907117i
$477$			34.2458i			1.56801i
$478$	−1.07133	−	1.42718i	−0.0490013	−	0.0652777i
$479$			20.1092i			0.918811i	0.888227	+	0.459405i	$0.151938\pi$
$479$			20.1092i			0.918811i	−0.888227	+	0.459405i	$0.848062\pi$
$480$	0.323497	+	4.13778i	0.0147655	+	0.188863i
$481$	−1.02105	+	0.362019i	−0.0465557	+	0.0165067i
$482$	−14.4283	−	19.2209i	−0.657193	−	0.875488i
$483$	1.06212			0.0483284
$484$	−4.07054	+	14.0001i	−0.185025	+	0.636368i
$485$		−	32.7844i		−	1.48866i
$486$	−4.68261	−	6.23800i	−0.212408	−	0.282961i
$487$		−	14.2922i		−	0.647643i	−0.946118	−	0.323822i	$-0.895032\pi$
$487$		−	14.2922i		−	0.647643i	0.946118	−	0.323822i	$-0.104968\pi$
$488$	16.4828	−	6.22247i	0.746139	−	0.281678i
$489$		−	0.784373i		−	0.0354706i
$490$	3.98424	−	2.99081i	0.179990	−	0.135111i
$491$		−	20.8674i		−	0.941734i	−0.882204	−	0.470867i	$-0.843941\pi$
$491$		−	20.8674i		−	0.941734i	0.882204	−	0.470867i	$-0.156059\pi$
$492$	0.341287	−	1.17381i	0.0153864	−	0.0529195i
$493$			22.3673i			1.00737i
$494$	−0.366326	+	0.551707i	−0.0164818	+	0.0248225i
$495$	20.0616			0.901701
$496$	2.47240	−	3.89232i	0.111014	−	0.174770i
$497$	−16.5533			−0.742517
$498$	−0.666545	−	0.887946i	−0.0298686	−	0.0397898i
$499$	19.1219			0.856016			0.428008	−	0.903775i	$-0.359216\pi$
$499$	19.1219			0.856016			0.428008	+	0.903775i	$0.359216\pi$
$500$	4.73959	−	16.3012i	0.211961	−	0.729011i
$501$	−4.85106			−0.216729
$502$	−13.9518	−	18.5861i	−0.622701	−	0.829538i
$503$	27.5342			1.22769			0.613844	−	0.789427i	$-0.289622\pi$
$503$	27.5342			1.22769			0.613844	+	0.789427i	$0.289622\pi$
$504$	−7.82365	+	2.95354i	−0.348493	+	0.131561i
$505$			32.2385i			1.43459i
$506$	11.1096	−	8.33950i	0.493880	−	0.370736i
$507$	1.70557	+	2.10286i	0.0757471	+	0.0933911i
$508$	−8.24390	+	28.3538i	−0.365764	+	1.25800i
$509$	−13.8266			−0.612851			−0.306426	−	0.951895i	$-0.599133\pi$
$509$	−13.8266			−0.612851			−0.306426	+	0.951895i	$0.599133\pi$
$510$	2.20782	+	2.94117i	0.0977639	+	0.130237i
$511$	−11.4665			−0.507246
$512$	−19.9875	−	10.6067i	−0.883330	−	0.468752i
$513$			0.161129i			0.00711401i
$514$	21.1253	−	15.8579i	0.931797	−	0.699462i
$515$	19.3748			0.853756
$516$	0.648850	−	2.23163i	0.0285640	−	0.0982422i
$517$			4.44705i			0.195581i
$518$	0.255093	+	0.339825i	0.0112081	+	0.0149310i
$519$	−4.13222			−0.181384
$520$	23.1901	+	27.4374i	1.01695	+	1.20321i
$521$	−4.40236			−0.192871			−0.0964355	−	0.995339i	$-0.530744\pi$
$521$	−4.40236			−0.192871			−0.0964355	+	0.995339i	$0.530744\pi$
$522$	15.8410	+	21.1028i	0.693341	+	0.923643i
$523$			5.70151i			0.249309i	0.992200	+	0.124655i	$0.0397823\pi$
$523$			5.70151i			0.249309i	−0.992200	+	0.124655i	$0.960218\pi$
$524$	−30.4402	−	8.85053i	−1.32979	−	0.386637i
$525$	−1.54322			−0.0673518
$526$	0.560082	−	0.420431i	0.0244207	−	0.0183317i
$527$		−	4.08591i		−	0.177985i
$528$	0.860393	−	1.35452i	0.0374438	−	0.0589481i
$529$	3.00612			0.130701
$530$	−34.6417	−	46.1484i	−1.50474	−	2.00456i
$531$	−20.9601			−0.909593
$532$	0.249427	+	0.0725211i	0.0108140	+	0.00314419i
$533$	−3.53587	−	9.97265i	−0.153156	−	0.431963i
$534$	0.231430	−	0.173725i	0.0100149	−	0.00751782i
$535$		−	23.0345i		−	0.995869i
$536$	−8.03271	−	21.2779i	−0.346960	−	0.919066i
$537$	0.0825646			0.00356292
$538$	−8.51238	−	11.3399i	−0.366995	−	0.488896i
$539$	−1.92616			−0.0829654
$540$	8.39312	+	2.44031i	0.361182	+	0.105014i
$541$	−21.6901			−0.932529			−0.466265	−	0.884645i	$-0.654400\pi$
$541$	−21.6901			−0.932529			−0.466265	+	0.884645i	$0.654400\pi$
$542$	16.8938	+	22.5053i	0.725650	+	0.966684i
$543$	4.38312			0.188098
$544$	−19.9889	+	1.56276i	−0.857018	+	0.0670028i
$545$	−42.5810			−1.82397
$546$	0.587449	−	0.884730i	0.0251405	−	0.0378630i
$547$			8.57481i			0.366632i	0.983054	+	0.183316i	$0.0586832\pi$
$547$			8.57481i			0.366632i	−0.983054	+	0.183316i	$0.941317\pi$
$548$	−16.1215	−	4.68733i	−0.688674	−	0.200233i
$549$		−	18.4167i		−	0.786006i
$550$	−16.1417	+	12.1169i	−0.688286	+	0.516668i
$551$		−	0.819618i		−	0.0349169i
$552$	2.81054	−	1.06102i	0.119624	−	0.0451599i
$553$			14.6896i			0.624667i
$554$	24.6708	+	32.8655i	1.04816	+	1.39632i
$555$		−	0.220446i		−	0.00935743i
$556$	−25.9741	−	7.55200i	−1.10155	−	0.320276i
$557$	−2.70216			−0.114494			−0.0572471	−	0.998360i	$-0.518232\pi$
$557$	−2.70216			−0.114494			−0.0572471	+	0.998360i	$0.518232\pi$
$558$	−2.89373	−	3.85491i	−0.122501	−	0.163191i
$559$	−6.72235	−	18.9599i	−0.284325	−	0.801917i
$560$	7.55519	−	11.8942i	0.319265	−	0.502621i
$561$		−	1.42189i		−	0.0600324i
$562$	−12.3123	−	16.4020i	−0.519364	−	0.691877i
$563$		−	39.2914i		−	1.65593i	−0.560777	−	0.827967i	$-0.689497\pi$
$563$		−	39.2914i		−	1.65593i	0.560777	−	0.827967i	$-0.310503\pi$
$564$	−0.268502	+	0.923477i	−0.0113060	+	0.0388854i
$565$	−16.4970			−0.694035
$566$	−4.70994	−	6.27441i	−0.197974	−	0.263733i
$567$			8.61147i			0.361648i
$568$	−43.8025	+	16.5360i	−1.83791	+	0.693837i
$569$	1.67637			0.0702771			0.0351386	−	0.999382i	$-0.488813\pi$
$569$	1.67637			0.0702771			0.0351386	+	0.999382i	$0.488813\pi$
$570$	−0.0809024	−	0.107775i	−0.00338863	−	0.00451420i
$571$		−	34.5286i		−	1.44498i	−0.691384	−	0.722488i	$-0.742999\pi$
$571$		−	34.5286i		−	1.44498i	0.691384	−	0.722488i	$-0.257001\pi$
$572$	−0.802078	−	13.8665i	−0.0335366	−	0.579789i
$573$			1.12035i			0.0468034i
$574$	−3.31910	+	2.49151i	−0.138536	+	0.103994i
$575$	−37.7858			−1.57578
$576$	−17.7521	+	15.6310i	−0.739669	+	0.651291i
$577$		−	22.3246i		−	0.929384i	−0.885472	−	0.464692i	$-0.846165\pi$
$577$		−	22.3246i		−	0.929384i	0.885472	−	0.464692i	$-0.153835\pi$
$578$	5.01891	−	3.76749i	0.208759	−	0.156707i
$579$	4.80785			0.199808
$580$	−42.6935	−	12.4132i	−1.77275	−	0.515430i
$581$			3.76948i			0.156384i
$582$	−2.19227	+	1.64565i	−0.0908727	+	0.0682144i
$583$			22.3102i			0.923993i
$584$	−30.3419	+	11.4545i	−1.25556	+	0.473990i
$585$	35.3942	−	12.5492i	1.46337	−	0.518848i
$586$	27.9543	−	20.9842i	1.15478	−	0.866848i
$587$	13.2895			0.548517			0.274259	−	0.961656i	$-0.411568\pi$
$587$	13.2895			0.548517			0.274259	+	0.961656i	$0.411568\pi$
$588$	−0.399987	−	0.116297i	−0.0164952	−	0.00479599i
$589$			0.149722i			0.00616920i
$590$	28.2451	−	21.2025i	1.16283	−	0.872893i
$591$			1.73250i			0.0712655i
$592$	1.01448	+	0.644399i	0.0416950	+	0.0264846i
$593$			22.1464i			0.909444i	0.890634	+	0.454722i	$0.150261\pi$
$593$			22.1464i			0.909444i	−0.890634	+	0.454722i	$0.849739\pi$
$594$	−2.02880	−	2.70269i	−0.0832428	−	0.110893i
$595$		−	12.4858i		−	0.511867i
$596$	10.8062	−	37.1666i	0.442640	−	1.52240i
$597$		−	3.92522i		−	0.160649i
$598$	14.3837	−	21.6626i	0.588192	−	0.885850i
$599$	23.3029			0.952129			0.476065	−	0.879410i	$-0.342063\pi$
$599$	23.3029			0.952129			0.476065	+	0.879410i	$0.342063\pi$
$600$	−4.08359	+	1.54161i	−0.166712	+	0.0629361i
$601$	−14.8316			−0.604993			−0.302496	−	0.953151i	$-0.597820\pi$
$601$	−14.8316			−0.604993			−0.302496	+	0.953151i	$0.597820\pi$
$602$	−6.31022	+	4.73683i	−0.257186	+	0.193059i
$603$	−23.7745			−0.968172
$604$	−10.6759	−	3.10403i	−0.434397	−	0.126301i
$605$	−25.6803			−1.04405
$606$	2.15577	−	1.61825i	0.0875721	−	0.0657368i
$607$	38.0443			1.54417			0.772085	−	0.635520i	$-0.219214\pi$
$607$	38.0443			1.54417			0.772085	+	0.635520i	$0.219214\pi$
$608$	0.732465	−	0.0572651i	0.0297054	−	0.00232241i
$609$			1.31436i			0.0532605i
$610$	18.6296	+	24.8177i	0.754292	+	1.00484i
$611$	2.78179	+	7.84583i	0.112539	+	0.317408i
$612$	−5.85144	+	20.1252i	−0.236530	+	0.813515i
$613$	17.0574			0.688941			0.344470	−	0.938797i	$-0.388059\pi$
$613$	17.0574			0.688941			0.344470	+	0.938797i	$0.388059\pi$
$614$	−16.9389	+	12.7154i	−0.683600	+	0.513151i
$615$	2.15312			0.0868221
$616$	−5.09689	+	1.92415i	−0.205360	+	0.0775261i
$617$		−	7.95481i		−	0.320249i	−0.987097	−	0.160124i	$-0.948810\pi$
$617$		−	7.95481i		−	0.320249i	0.987097	−	0.160124i	$-0.0511895\pi$
$618$	−0.972541	−	1.29558i	−0.0391213	−	0.0521159i
$619$	27.3721			1.10018			0.550088	−	0.835106i	$-0.314594\pi$
$619$	27.3721			1.10018			0.550088	+	0.835106i	$0.314594\pi$
$620$	7.79897	+	2.26756i	0.313214	+	0.0910674i
$621$		−	6.32668i		−	0.253881i
$622$	25.1428	−	18.8737i	1.00813	−	0.756766i
$623$	−0.982458			−0.0393614
$624$	0.670668	−	2.92796i	0.0268482	−	0.117212i
$625$	−7.14645			−0.285858
$626$	−9.43995	+	7.08619i	−0.377296	+	0.283221i
$627$			0.0521032i			0.00208080i
$628$	30.9966	+	9.01231i	1.23690	+	0.359630i
$629$	1.06494			0.0424619
$630$	−8.84268	−	11.7799i	−0.352301	−	0.469322i
$631$		−	21.1834i		−	0.843298i	−0.906759	−	0.421649i	$-0.861452\pi$
$631$		−	21.1834i		−	0.843298i	0.906759	−	0.421649i	$-0.138548\pi$
$632$	14.6743	+	38.8709i	0.583713	+	1.54620i
$633$	4.05416			0.161138
$634$	−22.2031	+	16.6670i	−0.881797	+	0.661929i
$635$	−52.0093			−2.06393
$636$	−1.34703	+	4.63294i	−0.0534134	+	0.183708i
$637$	−3.39827	+	1.20488i	−0.134644	+	0.0477391i
$638$	10.3200	+	13.7479i	0.408571	+	0.544283i
$639$			48.9419i			1.93611i
$640$	8.11034	−	39.0211i	0.320590	−	1.54244i
$641$	0.478600			0.0189036			0.00945179	−	0.999955i	$-0.496991\pi$
$641$	0.478600			0.0189036			0.00945179	+	0.999955i	$0.496991\pi$
$642$	−1.54030	+	1.15624i	−0.0607910	+	0.0456333i
$643$	−5.62114			−0.221676			−0.110838	−	0.993838i	$-0.535353\pi$
$643$	−5.62114			−0.221676			−0.110838	+	0.993838i	$0.535353\pi$
$644$	−9.79368	−	2.84752i	−0.385925	−	0.112208i
$645$	4.09348			0.161181
$646$	0.520643	−	0.390826i	0.0204844	−	0.0153768i
$647$	−44.2220			−1.73854			−0.869272	−	0.494333i	$-0.835412\pi$
$647$	−44.2220			−1.73854			−0.869272	+	0.494333i	$0.835412\pi$
$648$	8.60249	+	22.7872i	0.337938	+	0.895166i
$649$	−13.6550			−0.536004
$650$	−20.8989	+	31.4749i	−0.819722	+	1.23455i
$651$		−	0.240098i		−	0.00941019i
$652$	−2.10288	+	7.23257i	−0.0823551	+	0.283249i
$653$			4.90631i			0.191999i	0.995381	+	0.0959994i	$0.0306047\pi$
$653$			4.90631i			0.191999i	−0.995381	+	0.0959994i	$0.969395\pi$
$654$	2.13740	+	2.84737i	0.0835791	+	0.111341i
$655$		−	55.8364i		−	2.18171i
$656$	−6.29390	+	9.90853i	−0.245735	+	0.386863i
$657$			33.9020i			1.32264i
$658$	2.61125	−	1.96016i	0.101797	−	0.0764149i
$659$		−	2.44724i		−	0.0953310i	−0.998863	−	0.0476655i	$-0.984822\pi$
$659$		−	2.44724i		−	0.0953310i	0.998863	−	0.0476655i	$-0.0151782\pi$
$660$	2.71403	+	0.789108i	0.105644	+	0.0307160i
$661$	−46.9632			−1.82666			−0.913328	−	0.407225i	$-0.866497\pi$
$661$	−46.9632			−1.82666			−0.913328	+	0.407225i	$0.866497\pi$
$662$	38.0516	−	28.5638i	1.47892	−	1.11016i
$663$	−0.889446	−	2.50861i	−0.0345432	−	0.0974264i
$664$	3.76555	+	9.97459i	0.146132	+	0.387089i
$665$			0.457523i			0.0177420i
$666$	1.00473	−	0.754212i	0.0389326	−	0.0292251i
$667$			32.1821i			1.24609i
$668$	44.7308	+	13.0055i	1.73069	+	0.503199i
$669$	−3.67558			−0.142106
$670$	32.0376	−	24.0494i	1.23772	−	0.929108i
$671$		−	11.9980i		−	0.463177i
$672$	−1.17460	+	0.0918317i	−0.0453111	+	0.00354248i
$673$	42.5580			1.64049			0.820245	−	0.572013i	$-0.193837\pi$
$673$	42.5580			1.64049			0.820245	+	0.572013i	$0.193837\pi$
$674$	−0.0162120	+	0.0121697i	−0.000624464	+	0.000468760i
$675$			9.19240i			0.353816i
$676$	−10.0891	−	23.9627i	−0.388043	−	0.921641i
$677$		−	27.1383i		−	1.04301i	−0.853249	−	0.521504i	$-0.825371\pi$
$677$		−	27.1383i		−	1.04301i	0.853249	−	0.521504i	$-0.174629\pi$
$678$	0.828087	+	1.10315i	0.0318025	+	0.0423661i
$679$	9.30657			0.357153
$680$	−12.4727	−	33.0392i	−0.478308	−	1.26699i
$681$		−	3.76648i		−	0.144332i
$682$	−1.88518	−	2.51137i	−0.0721874	−	0.0961653i
$683$	−34.5690			−1.32275			−0.661373	−	0.750057i	$-0.730026\pi$
$683$	−34.5690			−1.32275			−0.661373	+	0.750057i	$0.730026\pi$
$684$	0.214418	−	0.737461i	0.00819846	−	0.0281975i
$685$		−	29.5715i		−	1.12987i
$686$	0.849005	+	1.13101i	0.0324152	+	0.0431823i
$687$		−	0.886732i		−	0.0338309i
$688$	−11.9659	+	18.8380i	−0.456195	+	0.718191i
$689$	13.9558	+	39.3613i	0.531675	+	1.49955i
$690$	3.17661	+	4.23176i	0.120931	+	0.161100i
$691$	26.6922			1.01542			0.507709	−	0.861529i	$-0.330492\pi$
$691$	26.6922			1.01542			0.507709	+	0.861529i	$0.330492\pi$
$692$	38.1025	+	11.0783i	1.44844	+	0.421136i
$693$			5.69492i			0.216332i
$694$	−2.65974	−	3.54320i	−0.100962	−	0.134498i
$695$		−	47.6442i		−	1.80725i
$696$	1.31299	+	3.47799i	0.0497687	+	0.131833i
$697$			10.4014i			0.393979i
$698$	−1.40722	+	1.05634i	−0.0532640	+	0.0399831i
$699$		−	2.50904i		−	0.0949007i
$700$	14.2298	+	4.13733i	0.537836	+	0.156377i
$701$			21.2235i			0.801602i	0.916165	+	0.400801i	$0.131268\pi$
$701$			21.2235i			0.801602i	−0.916165	+	0.400801i	$0.868732\pi$
$702$	−5.27000	−	3.49921i	−0.198903	−	0.132069i
$703$	−0.0390232			−0.00147179
$704$	−11.5650	+	10.1831i	−0.435871	+	0.383792i
$705$	−1.69393			−0.0637972
$706$	6.28777	+	8.37633i	0.236643	+	0.315247i
$707$	−9.15160			−0.344181
$708$	−2.83560	−	0.824453i	−0.106568	−	0.0309848i
$709$	−38.7261			−1.45439			−0.727194	−	0.686432i	$-0.759176\pi$
$709$	−38.7261			−1.45439			−0.727194	+	0.686432i	$0.759176\pi$
$710$	−49.5077	−	65.9523i	−1.85799	−	2.47515i
$711$	43.4317			1.62882
$712$	−2.59973	+	0.981433i	−0.0974289	+	0.0367808i
$713$		−	5.87881i		−	0.220163i
$714$	−0.834916	+	0.626738i	−0.0312459	+	0.0234551i
$715$	23.0583	−	8.17549i	0.862332	−	0.305746i
$716$	−0.761314	−	0.221353i	−0.0284516	−	0.00827235i
$717$	−0.262814			−0.00981499
$718$	30.6967	+	40.8930i	1.14559	+	1.52611i
$719$	44.9233			1.67536			0.837679	−	0.546163i	$-0.183912\pi$
$719$	44.9233			1.67536			0.837679	+	0.546163i	$0.183912\pi$
$720$	−35.1666	−	22.3378i	−1.31058	−	0.832482i
$721$			5.49996i			0.204829i
$722$	21.4702	−	16.1168i	0.799037	−	0.599805i
$723$	−3.53951			−0.131636
$724$	−40.4161	−	11.7510i	−1.50205	−	0.436723i
$725$		−	46.7592i		−	1.73659i
$726$	1.28905	+	1.71723i	0.0478413	+	0.0637323i
$727$	24.2750			0.900310			0.450155	−	0.892950i	$-0.351369\pi$
$727$	24.2750			0.900310			0.450155	+	0.892950i	$0.351369\pi$
$728$	−7.78870	+	6.58302i	−0.288668	+	0.243983i
$729$	24.6857			0.914285
$730$	−34.2940	−	45.6851i	−1.26928	−	1.69088i
$731$			19.7749i			0.731402i
$732$	0.724408	−	2.49151i	0.0267749	−	0.0920887i
$733$	−21.7151			−0.802067			−0.401033	−	0.916063i	$-0.631349\pi$
$733$	−21.7151			−0.802067			−0.401033	+	0.916063i	$0.631349\pi$
$734$	−9.16348	+	6.87865i	−0.338230	+	0.253896i
$735$		−	0.733695i		−	0.0270627i
$736$	−28.7600	+	2.24850i	−1.06011	+	0.0828807i
$737$	−15.4884			−0.570523
$738$	7.36645	+	9.81331i	0.271163	+	0.361233i
$739$	4.13272			0.152025			0.0760123	−	0.997107i	$-0.475781\pi$
$739$	4.13272			0.152025			0.0760123	+	0.997107i	$0.475781\pi$
$740$	−0.591010	+	2.03270i	−0.0217260	+	0.0747235i
$741$	0.0325925	+	0.0919245i	0.00119731	+	0.00337693i
$742$	13.1002	−	9.83381i	0.480924	−	0.361011i
$743$		−	20.2682i		−	0.743567i	−0.928319	−	0.371784i	$-0.878746\pi$
$743$		−	20.2682i		−	0.743567i	0.928319	−	0.371784i	$-0.121254\pi$
$744$	−0.239848	−	0.635335i	−0.00879325	−	0.0232925i
$745$	68.1746			2.49772
$746$	−6.56750	−	8.74897i	−0.240453	−	0.320323i
$747$	11.1449			0.407771
$748$	−3.81205	+	13.1110i	−0.139382	+	0.479387i
$749$	6.53885			0.238924
$750$	−1.50093	−	1.99948i	−0.0548061	−	0.0730106i
$751$	50.2644			1.83417			0.917087	−	0.398687i	$-0.130534\pi$
$751$	50.2644			1.83417			0.917087	+	0.398687i	$0.130534\pi$
$752$	4.95163	−	7.79538i	0.180567	−	0.284268i
$753$	−3.42262			−0.124727
$754$	26.8071	+	17.7995i	0.976256	+	0.648221i
$755$		−	19.5828i		−	0.712691i
$756$	−0.692735	+	2.38257i	−0.0251945	+	0.0866532i
$757$		−	20.4735i		−	0.744122i	−0.928208	−	0.372061i	$-0.878651\pi$
$757$		−	20.4735i		−	0.744122i	0.928208	−	0.372061i	$-0.121349\pi$
$758$	−36.7125	+	27.5586i	−1.33346	+	1.00097i
$759$		−	2.04582i		−	0.0742585i
$760$	0.457046	+	1.21067i	0.0165788	+	0.0439157i
$761$		−	31.2031i		−	1.13111i	−0.824710	−	0.565556i	$-0.808662\pi$
$761$		−	31.2031i		−	1.13111i	0.824710	−	0.565556i	$-0.191338\pi$
$762$	2.61067	+	3.47783i	0.0945744	+	0.125988i
$763$		−	12.0875i		−	0.437599i
$764$	3.00363	−	10.3306i	0.108668	−	0.373748i
$765$	−36.9157			−1.33469
$766$	−30.3829	−	40.4750i	−1.09778	−	1.46242i
$767$	−24.0911	+	8.54167i	−0.869880	+	0.308422i
$768$	−3.01642	+	1.41637i	−0.108846	+	0.0511090i
$769$			32.8772i			1.18558i	0.805356	+	0.592791i	$0.201974\pi$
$769$			32.8772i			1.18558i	−0.805356	+	0.592791i	$0.798026\pi$
$770$	−5.76076	−	7.67427i	−0.207603	−	0.276561i
$771$		−	3.89021i		−	0.140103i
$772$	−44.3324	−	12.8897i	−1.59556	−	0.463911i
$773$	12.3295			0.443463			0.221731	−	0.975108i	$-0.428829\pi$
$773$	12.3295			0.443463			0.221731	+	0.975108i	$0.428829\pi$
$774$	14.0050	+	18.6569i	0.503400	+	0.670610i
$775$			8.54166i			0.306826i
$776$	24.6265	−	9.29686i	0.884041	−	0.333738i
$777$	0.0625785			0.00224499
$778$	−5.36724	−	7.15004i	−0.192425	−	0.256341i
$779$		−	0.381143i		−	0.0136558i
$780$	5.28192	−	0.305521i	0.189123	−	0.0109394i
$781$			31.8843i			1.14091i
$782$	−20.4429	+	15.3457i	−0.731037	+	0.548760i
$783$	7.82914			0.279791
$784$	3.37642	+	2.14470i	0.120587	+	0.0765966i
$785$			56.8571i			2.02932i
$786$	−3.73375	+	2.80277i	−0.133178	+	0.0999717i
$787$	34.8281			1.24149			0.620743	−	0.784014i	$-0.286831\pi$
$787$	34.8281			1.24149			0.620743	+	0.784014i	$0.286831\pi$
$788$	4.64478	−	15.9751i	0.165463	−	0.569089i
$789$		−	0.103139i		−	0.00367184i
$790$	−58.5270	+	43.9339i	−2.08230	+	1.56310i
$791$		−	4.68304i		−	0.166510i
$792$	5.68897	+	15.0696i	0.202149	+	0.535474i
$793$	−7.50517	−	21.1677i	−0.266516	−	0.751689i
$794$	11.6203	−	8.72288i	0.412388	−	0.309563i
$795$	−8.49820			−0.301400
$796$	−10.5234	+	36.1938i	−0.372992	+	1.28286i
$797$			37.3680i			1.32364i	0.749661	+	0.661821i	$0.230216\pi$
$797$			37.3680i			1.32364i	−0.749661	+	0.661821i	$0.769784\pi$
$798$	0.0305943	−	0.0229659i	0.00108303	−	0.000812984i
$799$		−	8.18310i		−	0.289497i
$800$	41.7872	−	3.26697i	1.47740	−	0.115505i
$801$			2.90476i			0.102635i
$802$	1.52720	+	2.03448i	0.0539274	+	0.0718400i
$803$			22.0862i			0.779405i
$804$	−3.21633	−	0.935153i	−0.113431	−	0.0329803i
$805$		−	17.9645i		−	0.633166i
$806$	−4.89694	−	3.25150i	−0.172487	−	0.114529i
$807$	−2.08823			−0.0735091
$808$	−24.2165	+	9.14205i	−0.851932	+	0.321616i
$809$	36.3556			1.27819			0.639097	−	0.769126i	$-0.279308\pi$
$809$	36.3556			1.27819			0.639097	+	0.769126i	$0.279308\pi$
$810$	−34.3102	+	25.7552i	−1.20554	+	0.904947i
$811$	−29.4704			−1.03485			−0.517423	−	0.855730i	$-0.673109\pi$
$811$	−29.4704			−1.03485			−0.517423	+	0.855730i	$0.673109\pi$
$812$	3.52376	−	12.1195i	0.123660	−	0.425311i
$813$	4.14433			0.145348
$814$	0.654556	−	0.491348i	0.0229422	−	0.0172218i
$815$	−13.2667			−0.464712
$816$	−1.58323	+	2.49248i	−0.0554240	+	0.0872544i
$817$		−	0.724623i		−	0.0253514i
$818$	−18.6019	−	24.7808i	−0.650400	−	0.866439i
$819$	3.56238	+	10.0474i	0.124480	+	0.351085i
$820$	−19.8535	−	5.77244i	−0.693316	−	0.201582i
$821$	8.34090			0.291100			0.145550	−	0.989351i	$-0.453505\pi$
$821$	8.34090			0.291100			0.145550	+	0.989351i	$0.453505\pi$
$822$	−1.97743	+	1.48438i	−0.0689709	+	0.0517736i
$823$	46.3329			1.61506			0.807531	−	0.589825i	$-0.200803\pi$
$823$	46.3329			1.61506			0.807531	+	0.589825i	$0.200803\pi$
$824$	5.49422	+	14.5537i	0.191400	+	0.507002i
$825$			2.97249i			0.103489i
$826$	6.01879	+	8.01800i	0.209420	+	0.278982i
$827$	36.3252			1.26315			0.631575	−	0.775315i	$-0.282409\pi$
$827$	36.3252			1.26315			0.631575	+	0.775315i	$0.282409\pi$
$828$	−8.41905	+	28.9562i	−0.292582	+	1.00630i
$829$			12.3282i			0.428175i	0.976814	+	0.214088i	$0.0686778\pi$
$829$			12.3282i			0.428175i	−0.976814	+	0.214088i	$0.931322\pi$
$830$	−15.0185	+	11.2738i	−0.521300	+	0.391319i
$831$	6.05217			0.209947
$832$	−14.0339	+	25.2002i	−0.486537	+	0.873660i
$833$	3.54436			0.122805
$834$	−3.18594	+	2.39156i	−0.110320	+	0.0828128i
$835$			82.0496i			2.83944i
$836$	0.139687	−	0.480435i	0.00483118	−	0.0166162i
$837$	−1.43017			−0.0494341
$838$	−16.0366	−	21.3633i	−0.553975	−	0.737985i
$839$			33.9276i			1.17131i	0.810560	+	0.585656i	$0.199163\pi$
$839$			33.9276i			1.17131i	−0.810560	+	0.585656i	$0.800837\pi$
$840$	−0.732929	−	1.94146i	−0.0252885	−	0.0669869i
$841$	−10.8247			−0.373266
$842$	−7.17141	+	5.38329i	−0.247143	+	0.185520i
$843$	−3.02042			−0.104029
$844$	−37.3827	−	10.8691i	−1.28677	−	0.374129i
$845$	35.5672	−	28.8476i	1.22355	−	0.992389i
$846$	−5.79544	−	7.72047i	−0.199251	−	0.265435i
$847$		−	7.28992i		−	0.250485i
$848$	24.8416	−	39.1083i	0.853063	−	1.34298i
$849$	−1.15543			−0.0396542
$850$	29.7027	−	22.2966i	1.01879	−	0.764768i
$851$	1.53223			0.0525243
$852$	−1.92509	+	6.62110i	−0.0659526	+	0.226835i
$853$	38.7697			1.32745			0.663725	−	0.747977i	$-0.268974\pi$
$853$	38.7697			1.32745			0.663725	+	0.747977i	$0.268974\pi$
$854$	−7.04504	+	5.28843i	−0.241076	+	0.180966i
$855$	1.35272			0.0462621
$856$	17.3027	−	6.53203i	0.591396	−	0.223260i
$857$	−26.4866			−0.904764			−0.452382	−	0.891824i	$-0.649426\pi$
$857$	−26.4866			−0.904764			−0.452382	+	0.891824i	$0.649426\pi$
$858$	−1.70413	−	1.13152i	−0.0581780	−	0.0386294i
$859$		−	17.8500i		−	0.609033i	−0.952507	−	0.304517i	$-0.901505\pi$
$859$		−	17.8500i		−	0.609033i	0.952507	−	0.304517i	$-0.0984949\pi$
$860$	−37.7453	−	10.9745i	−1.28710	−	0.374227i
$861$			0.611209i			0.0208300i
$862$	23.1502	+	30.8398i	0.788498	+	1.05041i
$863$			13.6999i			0.466350i	0.972435	+	0.233175i	$0.0749115\pi$
$863$			13.6999i			0.466350i	−0.972435	+	0.233175i	$0.925088\pi$
$864$	0.547006	+	6.99664i	0.0186095	+	0.238031i
$865$			69.8913i			2.37638i
$866$	−20.2405	+	15.1937i	−0.687801	+	0.516304i
$867$		−	0.924228i		−	0.0313884i
$868$	−0.643696	+	2.21391i	−0.0218485	+	0.0751449i
$869$	28.2945			0.959827
$870$	−5.23672	+	3.93099i	−0.177541	+	0.133273i
$871$	−27.3258	+	9.68857i	−0.925901	+	0.328285i
$872$	−12.0749	−	31.9854i	−0.408909	−	1.08316i
$873$		−	27.5160i		−	0.931276i
$874$	0.749101	−	0.562320i	0.0253387	−	0.0190208i
$875$			8.48812i			0.286951i
$876$	−1.33351	+	4.58643i	−0.0450552	+	0.154961i
$877$	1.66862			0.0563452			0.0281726	−	0.999603i	$-0.491031\pi$
$877$	1.66862			0.0563452			0.0281726	+	0.999603i	$0.491031\pi$
$878$	−18.6011	+	13.9631i	−0.627757	+	0.471231i
$879$		−	5.14777i		−	0.173630i
$880$	−22.9101	−	14.5525i	−0.772298	−	0.490564i
$881$	−0.959187			−0.0323158			−0.0161579	−	0.999869i	$-0.505143\pi$
$881$	−0.959187			−0.0323158			−0.0161579	+	0.999869i	$0.505143\pi$
$882$	3.34398	−	2.51019i	0.112598	−	0.0845224i
$883$		−	40.6249i		−	1.36714i	−0.729886	−	0.683569i	$-0.760427\pi$
$883$		−	40.6249i		−	1.36714i	0.729886	−	0.683569i	$-0.239573\pi$
$884$	1.47592	+	25.5161i	0.0496405	+	0.858198i
$885$		−	5.20133i		−	0.174841i
$886$	18.2428	+	24.3024i	0.612879	+	0.816454i
$887$	−58.6312			−1.96864			−0.984322	−	0.176380i	$-0.943561\pi$
$887$	−58.6312			−1.96864			−0.984322	+	0.176380i	$0.943561\pi$
$888$	0.165592	−	0.0625132i	0.00555690	−	0.00209781i
$889$		−	14.7640i		−	0.495168i
$890$	−2.93834	−	3.91435i	−0.0984934	−	0.131209i
$891$	16.5870			0.555687
$892$	33.8919	+	9.85412i	1.13479	+	0.329940i
$893$			0.299858i			0.0100344i
$894$	−3.42210	−	4.55879i	−0.114452	−	0.152469i
$895$		−	1.39648i		−	0.0466791i
$896$	11.0770	+	2.30230i	0.370056	+	0.0769144i
$897$	−1.27973	−	3.60939i	−0.0427291	−	0.120514i
$898$	−9.87368	−	13.1533i	−0.329489	−	0.438933i
$899$	7.27491			0.242632
$900$	12.2325	−	42.0722i	0.407751	−	1.40241i
$901$		−	41.0534i		−	1.36769i
$902$	4.79904	+	6.39310i	0.159791	+	0.212867i
$903$			1.16202i			0.0386697i
$904$	−4.67815	−	12.3920i	−0.155593	−	0.412152i
$905$		−	74.1351i		−	2.46433i
$906$	−1.30949	+	0.982981i	−0.0435049	+	0.0326574i
$907$			16.8426i			0.559251i	0.960109	+	0.279625i	$0.0902103\pi$
$907$			16.8426i			0.559251i	−0.960109	+	0.279625i	$0.909790\pi$
$908$	−10.0978	+	34.7301i	−0.335108	+	1.15256i
$909$			27.0578i			0.897451i
$910$	−14.9641	−	9.93596i	−0.496055	−	0.329374i
$911$	−19.4339			−0.643874			−0.321937	−	0.946761i	$-0.604334\pi$
$911$	−19.4339			−0.643874			−0.321937	+	0.946761i	$0.604334\pi$
$912$	0.0580150	−	0.0913335i	0.00192107	−	0.00302435i
$913$	7.26061			0.240291
$914$	−17.1246	−	22.8128i	−0.566433	−	0.754580i
$915$	4.57016			0.151085
$916$	−2.37730	+	8.17641i	−0.0785482	+	0.270156i
$917$	15.8504			0.523426
$918$	3.73324	+	4.97328i	0.123215	+	0.164143i
$919$	−4.84960			−0.159974			−0.0799868	−	0.996796i	$-0.525488\pi$
$919$	−4.84960			−0.159974			−0.0799868	+	0.996796i	$0.525488\pi$
$920$	−17.9458	−	47.5367i	−0.591655	−	1.56724i
$921$			3.11929i			0.102784i
$922$	17.3106	−	12.9944i	0.570096	−	0.427948i
$923$	19.9448	+	56.2527i	0.656490	+	1.85158i
$924$	−0.224006	+	0.770437i	−0.00736924	+	0.0253455i
$925$	−2.22627			−0.0731994
$926$	19.0141	+	25.3299i	0.624842	+	0.832391i
$927$	16.2613			0.534091
$928$	−2.78247	−	35.5900i	−0.0913391	−	1.16830i
$929$			15.2435i			0.500124i	0.968230	+	0.250062i	$0.0804509\pi$
$929$			15.2435i			0.500124i	−0.968230	+	0.250062i	$0.919549\pi$
$930$	0.956609	−	0.718087i	0.0313684	−	0.0235470i
$931$	−0.129878			−0.00425658
$932$	−6.72667	+	23.1355i	−0.220339	+	0.757828i
$933$		−	4.63003i		−	0.151580i
$934$	8.59173	+	11.4456i	0.281130	+	0.374511i
$935$	−24.0495			−0.786504
$936$	19.4635	+	23.0282i	0.636184	+	0.752702i
$937$	−58.4300			−1.90883			−0.954413	−	0.298490i	$-0.903517\pi$
$937$	−58.4300			−1.90883			−0.954413	+	0.298490i	$0.903517\pi$
$938$	6.82694	+	9.09458i	0.222907	+	0.296949i
$939$			1.73836i			0.0567293i
$940$	15.6195	+	4.54138i	0.509451	+	0.148123i
$941$	−22.9904			−0.749467			−0.374733	−	0.927133i	$-0.622266\pi$
$941$	−22.9904			−0.749467			−0.374733	+	0.927133i	$0.622266\pi$
$942$	3.80200	−	2.85401i	0.123876	−	0.0929885i
$943$			14.9655i			0.487342i
$944$	23.9362	+	15.2043i	0.779058	+	0.494857i
$945$	−4.37034			−0.142167
$946$	9.12388	+	12.1545i	0.296643	+	0.395176i
$947$	−19.1597			−0.622608			−0.311304	−	0.950310i	$-0.600766\pi$
$947$	−19.1597			−0.622608			−0.311304	+	0.950310i	$0.600766\pi$
$948$	5.87566	+	1.70836i	0.190833	+	0.0554848i
$949$	13.8157	+	38.9662i	0.448477	+	1.26490i
$950$	−1.08841	+	0.817028i	−0.0353128	+	0.0265079i
$951$			4.08868i			0.132585i
$952$	9.37888	−	3.54066i	0.303971	−	0.114753i
$953$	40.8834			1.32434			0.662171	−	0.749353i	$-0.269635\pi$
$953$	40.8834			1.32434			0.662171	+	0.749353i	$0.269635\pi$
$954$	−29.0749	−	38.7324i	−0.941333	−	1.25401i
$955$	18.9494			0.613188
$956$	2.42337	+	0.704597i	0.0783773	+	0.0227883i
$957$	2.53166			0.0818370
$958$	−17.0728	−	22.7437i	−0.551597	−	0.734816i
$959$	8.39453			0.271073
$960$	−3.87888	−	4.40523i	−0.125190	−	0.142178i
$961$	29.6711			0.957131
$962$	0.847461	−	1.27632i	0.0273232	−	0.0411503i
$963$		−	19.3329i		−	0.622994i
$964$	32.6373	+	9.48933i	1.05118	+	0.305631i
$965$		−	81.3188i		−	2.61775i
$966$	−1.20128	+	0.901750i	−0.0386504	+	0.0290133i
$967$		−	1.86092i		−	0.0598431i	−0.999552	−	0.0299216i	$-0.990474\pi$
$967$		−	1.86092i		−	0.0598431i	0.999552	−	0.0299216i	$-0.00952575\pi$
$968$	−7.28231	−	19.2902i	−0.234062	−	0.620010i
$969$		−	0.0958761i		−	0.00307998i
$970$	27.8341	+	37.0796i	0.893700	+	1.19055i
$971$		−	22.8850i		−	0.734416i	−0.930139	−	0.367208i	$-0.880314\pi$
$971$		−	22.8850i		−	0.734416i	0.930139	−	0.367208i	$-0.119686\pi$
$972$	10.5922	+	3.07969i	0.339745	+	0.0987811i
$973$	13.5249			0.433587
$974$	12.1342	+	16.1647i	0.388805	+	0.517951i
$975$	1.85940	+	5.24430i	0.0595485	+	0.167952i
$976$	−13.3593	+	21.0316i	−0.427621	+	0.673207i
$977$		−	3.98677i		−	0.127548i	−0.997964	−	0.0637740i	$-0.979686\pi$
$977$		−	3.98677i		−	0.127548i	0.997964	−	0.0637740i	$-0.0203137\pi$
$978$	0.665937	+	0.887136i	0.0212943	+	0.0283675i
$979$			1.89237i			0.0604804i
$980$	−1.96701	+	6.76528i	−0.0628339	+	0.216109i
$981$	−35.7383			−1.14104
$982$	17.7166	+	23.6013i	0.565358	+	0.753148i
$983$			50.8782i			1.62276i	0.584518	+	0.811381i	$0.301284\pi$
$983$			50.8782i			1.62276i	−0.584518	+	0.811381i	$0.698716\pi$
$984$	0.610572	+	1.61735i	0.0194643	+	0.0515592i
$985$	29.3031			0.933673
$986$	−18.9900	−	25.2977i	−0.604764	−	0.805643i
$987$		−	0.480859i		−	0.0153059i
$988$	−0.0540829	−	0.935000i	−0.00172061	−	0.0297463i
$989$			28.4521i			0.904726i
$990$	−22.6899	+	17.0324i	−0.721132	+	0.541325i
$991$	−54.2500			−1.72331			−0.861653	−	0.507497i	$-0.830571\pi$
$991$	−54.2500			−1.72331			−0.861653	+	0.507497i	$0.830571\pi$
$992$	0.508283	+	6.50134i	0.0161380	+	0.206418i
$993$		−	7.00718i		−	0.222366i
$994$	18.7220	−	14.0538i	0.593826	−	0.445761i
$995$	−66.3902			−2.10471
$996$	1.50774	+	0.438378i	0.0477746	+	0.0138905i
$997$			25.8118i			0.817467i	0.912654	+	0.408734i	$0.134029\pi$
$997$			25.8118i			0.817467i	−0.912654	+	0.408734i	$0.865971\pi$
$998$	−21.6272	+	16.2346i	−0.684596	+	0.513898i
$999$		−	0.372756i		−	0.0117935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.i.a.701.16	yes	84
4.3	odd	2		2912.2.i.a.337.71		84
8.3	odd	2		2912.2.i.a.337.14		84
8.5	even	2	inner	728.2.i.a.701.70	yes	84
13.12	even	2	inner	728.2.i.a.701.69	yes	84
52.51	odd	2		2912.2.i.a.337.13		84
104.51	odd	2		2912.2.i.a.337.72		84
104.77	even	2	inner	728.2.i.a.701.15	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.i.a.701.15	✓	84	104.77	even	2	inner
728.2.i.a.701.16	yes	84	1.1	even	1	trivial
728.2.i.a.701.69	yes	84	13.12	even	2	inner
728.2.i.a.701.70	yes	84	8.5	even	2	inner
2912.2.i.a.337.13		84	52.51	odd	2
2912.2.i.a.337.14		84	8.3	odd	2
2912.2.i.a.337.71		84	4.3	odd	2
2912.2.i.a.337.72		84	104.51	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.13101 + 0.849005i) q^{2} +0.208275i q^{3} +(0.558380 - 1.92047i) q^{4} +3.52272 q^{5} +(-0.176827 - 0.235562i) q^{6} +1.00000i q^{7} +(0.998957 + 2.64615i) q^{8} +2.95662 q^{9} +(-3.98424 + 2.99081i) q^{10} +1.92616 q^{11} +(0.399987 + 0.116297i) q^{12} +(3.39827 - 1.20488i) q^{13} +(-0.849005 - 1.13101i) q^{14} +0.733695i q^{15} +(-3.37642 - 2.14470i) q^{16} -3.54436 q^{17} +(-3.34398 + 2.51019i) q^{18} +0.129878 q^{19} +(1.96701 - 6.76528i) q^{20} -0.208275 q^{21} +(-2.17851 + 1.63532i) q^{22} -5.09962 q^{23} +(-0.551127 + 0.208058i) q^{24} +7.40954 q^{25} +(-2.82054 + 4.24789i) q^{26} +1.24062i q^{27} +(1.92047 + 0.558380i) q^{28} -6.31068i q^{29} +(-0.622911 - 0.829818i) q^{30} +1.15279i q^{31} +(5.63964 - 0.440915i) q^{32} +0.401171i q^{33} +(4.00871 - 3.00918i) q^{34} +3.52272i q^{35} +(1.65092 - 5.67811i) q^{36} -0.300461 q^{37} +(-0.146894 + 0.110267i) q^{38} +(0.250947 + 0.707776i) q^{39} +(3.51904 + 9.32162i) q^{40} -2.93462i q^{41} +(0.235562 - 0.176827i) q^{42} -5.57927i q^{43} +(1.07553 - 3.69913i) q^{44} +10.4153 q^{45} +(5.76773 - 4.32960i) q^{46} +2.30877i q^{47} +(0.446689 - 0.703226i) q^{48} -1.00000 q^{49} +(-8.38028 + 6.29074i) q^{50} -0.738202i q^{51} +(-0.416414 - 7.19907i) q^{52} +11.5827i q^{53} +(-1.05329 - 1.40315i) q^{54} +6.78531 q^{55} +(-2.64615 + 0.998957i) q^{56} +0.0270504i q^{57} +(5.35780 + 7.13746i) q^{58} -7.08922 q^{59} +(1.40904 + 0.409680i) q^{60} -6.22897i q^{61} +(-0.978728 - 1.30382i) q^{62} +2.95662i q^{63} +(-6.00417 + 5.28677i) q^{64} +(11.9712 - 4.24446i) q^{65} +(-0.340596 - 0.453729i) q^{66} -8.04110 q^{67} +(-1.97910 + 6.80684i) q^{68} -1.06212i q^{69} +(-2.99081 - 3.98424i) q^{70} +16.5533i q^{71} +(2.95354 + 7.82365i) q^{72} +11.4665i q^{73} +(0.339825 - 0.255093i) q^{74} +1.54322i q^{75} +(0.0725211 - 0.249427i) q^{76} +1.92616i q^{77} +(-0.884730 - 0.587449i) q^{78} +14.6896 q^{79} +(-11.8942 - 7.55519i) q^{80} +8.61147 q^{81} +(2.49151 + 3.31910i) q^{82} +3.76948 q^{83} +(-0.116297 + 0.399987i) q^{84} -12.4858 q^{85} +(4.73683 + 6.31022i) q^{86} +1.31436 q^{87} +(1.92415 + 5.09689i) q^{88} +0.982458i q^{89} +(-11.7799 + 8.84268i) q^{90} +(1.20488 + 3.39827i) q^{91} +(-2.84752 + 9.79368i) q^{92} -0.240098 q^{93} +(-1.96016 - 2.61125i) q^{94} +0.457523 q^{95} +(0.0918317 + 1.17460i) q^{96} -9.30657i q^{97} +(1.13101 - 0.849005i) q^{98} +5.69492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 84 q^{9} + 8 q^{10} - 20 q^{12} - 8 q^{16} + 8 q^{17} - 12 q^{22} - 24 q^{23} + 92 q^{25} - 40 q^{30} + 44 q^{36} + 20 q^{38} - 24 q^{39} - 28 q^{40} - 72 q^{48} - 84 q^{49} - 44 q^{52} + 32 q^{55}+ \cdots - 16 q^{95}+O(q^{100}) \) 84 * q - 84 * q^9 + 8 * q^10 - 20 * q^12 - 8 * q^16 + 8 * q^17 - 12 * q^22 - 24 * q^23 + 92 * q^25 - 40 * q^30 + 44 * q^36 + 20 * q^38 - 24 * q^39 - 28 * q^40 - 72 * q^48 - 84 * q^49 - 44 * q^52 + 32 * q^55 - 40 * q^62 + 72 * q^64 - 24 * q^65 - 60 * q^66 - 92 * q^68 + 28 * q^74 + 12 * q^78 - 40 * q^79 + 84 * q^81 + 24 * q^82 - 48 * q^87 - 108 * q^88 + 20 * q^90 + 60 * q^92 + 36 * q^94 - 16 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more